Introduction to Environmental and Ecological Statistics
Environmental and Ecological Statistics is an incredibly broad term covering any form of statistics applied to environmental and ecological issues. Key themes include climate change, environmental regulation (e.g. water and air quality) and biodiversity monitoring. This course focuses on this theme rather than a particular type of statistical methodology. We will look at a variety of statistical methods, some of which you will know, and some which will be new.
The environment is (sometimes literally) a burning issue in the 21st century. This brings increased focus and interest in statistics as a subject, and how we are working to handle topics like climate change. Below, we see some examples of how climate change reporting can be presented.
1 Where’s the statistics?
We are interested in measuring, sampling or monitoring environmental and ecological data, including variation and uncertainty. This includes detecting and modelling environmental trends, including trends in time and space, modelling and understanding extreme data. We also wish to evaluate environmental regulation and policy, and risk assessment.
We want to understand changes in the environment, in either time, space or both. Are things getting better or worse? Where, when and by how much? What is going to happen next? Where do authorities need to take action, and how can we check if existing actions are working? Also, we should consider relationships between environmental variables (and other variables where necessary).
In general, there are no techniques that are unique to environmental statistics. However, the data used tend to be characterised by strong spatial and temporal elements, and often also high variability.
Our skills in presenting and communicating data are also crucial. We need to be able to explain our findings to the public and show them why our work is important. Below is an example of reporting of a winter storm in 2023, which makes use of plots to tell the story.
Some examples of environmental & ecological statistics include:
- Decision making: Is it safe to eat fish from a particular river?
- Prediction: What is the trend in temperature? Can we predict its level in 2060?
- Regulation: Have emission control agreements reduced air pollutants?
- Understanding: How did sea levels change over the past 100 years?
We will illustrate this with an example relating to air quality.
Only one person in ten lives in a city that complies with the World Health Organisation Air quality guidelines.
Fine particular matter was associated with an estimated 2,000 premature deaths and 22,500 lost life years in Scotland in 2010. There are 38 “Air Quality Management Areas” (AQMAs) which breach or are likely to breach legal limits. The Cleaner Air for Scotland strategy seeks to reduce air pollution across Scotland. It aims to achieve the “ambitious vision for Scotland to have the best air quality in Europe”.
There are 99 air quality monitoring stations in Scotland capturing PM\(_{2.5}\), PM\(_{10}\), NO\(_2\), NO\(_\text{X}\), SO\(_2\) and O\(_3\).
The map below shows the placement of the monitors. Live data are available at Scottish Air Quality.
The data from these monitors can be used to estimate the pollution levels across Scotland.
2 Quantification
Understanding and measuring quantities is a fundamental part of all science, not just statistics. As scientists, we use data to understand the process which we are investigating. These data have two main sources of uncertainty or error:
- Inherent variability of the process itself (the thing we are measuring is variable).
- Imprecise knowledge of the process (our measurements may not be accurate).
The plots below illustrate the trends in several climate change measures. Both sources of variability will be present, but how much of each?
A big part of our role as statisticians is to ask questions of both our data and our models. How were our data collected? Are they representative of the population? How much uncertainty do we have? Are our models valid? Are the assumptions reasonable? Does the model make sensible predictions? How much uncertainty do we have in our results? These skills are particularly crucial in applied areas such as environmental and ecological statistics.
Submarines have been used to measure Arctic sea ice. Over time, the ice has shrunk both in terms of thickness and extent. We may soon see ice-free summers, which will have a devastating impact on sea life.
This interactive map provides an illustration of the changes.
3 Understanding our data: trends
Much of the statistical analysis of environmental and ecological data will focus on identifying trends. The statistical definition of a trend is a long-term change in the mean level. Trends aren’t restricted to being linear, and we will also look at examples of non-linear trends, and changepoints.
Trends generally tend to focus on the mean of the data. However, we may also be interested in observing other aspects of the statistical distribution. Extreme value theory looks specifically at the limits of our distribution, and focuses on rare (or extreme) events.
We’ll cover this more later in the course.
4 Policy and legislation
A great deal of environmental statistical research is funded by governments and regulatory bodies. They need to know where the biggest challenges lie so that they can allocate their resources appropriately. Evidence-based policy relies on measuring changes and also evaluating the impacts of existing policies. However, the environment will be one of many competing policy areas, and every government will prioritise it differently.
COP is the United Nations Climate Change Conference that takes place annually (held in Glasgow in 2021), where most countries’ governments come together to try to agree on goals to limit global temperature rise and achieve net zero emissions. The most recent conference was COP29, which took place in Baku, Azerbaijan, in November 2024.
One of the key achievements of COP29 was an agreement by wealthier countries to pay at least US $300 billion per year to less wealthy countries to help finance their mitigation of climate change impacts, and to transform their economies away from fossil fuels. However, there was limited progress in other sectors.
A report on COP29 and its implications for the UK is available from the UK’s Climate Change Committee here.
Environmental policy tends to use very specific language: objectives, targets, guide values, standards, reductions relative to a baseline. Policy often prescribes monitoring quantities of interest over space and/or time. Quantities of interest include water, air and noise pollution, waste management, radioactive substances, biodiversity and animal and plant species.
Legislation is the legal framework used to implement policy. Most legislation focuses on setting targets or safe levels for the pollutants. A number of regulatory bodies exist specifically to monitor such things, e.g. Scottish Environment Protection Agency (SEPA, for Scotland), the Environment Agency (EA, for England) and the European Environment Agency (EEA, for the EU). As well as regulatory bodies, the Climate Change Committee advises governments within the UK on reducing emissions and addressing climate change impacts.
Much of our data come from routine monitoring of our environmental quantities of interest. Government agencies often make these data available to researchers and/or the public. These data are used to assess compliance with legislation as well as to identify environmental trends and their potential impacts on society.